Bohr Hamiltonian of triaxial nuclei using Morse plus screened Kratzer potentials with the extended Nikiforov–Uvarov method

In this work, Bohr Hamiltonian is used to explain the behavior of triaxial nuclei. A new potential, called Morse plus screened Kratzer potential, has been developed for the [Formula: see text]-part with [Formula: see text] fixed at [Formula: see text]. The Extended Nikiforov–Uvarov method involving Confluent Heun functions is used to derive the wave function and energy expression. The electric quadrupole transition rates and energy spectrum of platinum [Formula: see text] are determined and compared with the experimental data and some theoretical results.

Mass spectrum of triply heavy baryon in the hypercentral quark model

In this study, we consider baryons as three-body bound systems according to hypercentral constituent quark model in configuration space and solve three-body Klein–Gordon equation. Then we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we used screened potential and calculate the eigenfunctions and eigenvalues of triply heavy baryons by using Nikiforov–Uvarov method. We compute the ground and excited state masses of triply heavy baryons with quantum numbers [Formula: see text], [Formula: see text], [Formula: see text] via constituent quark model approach.

Vibrational energies of some diatomic molecules for a modified and deformed potential

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Study on energy and information-entropic measures of Hulthén potential in D dimension by an intuitive approximation to centrifugal term

Energy spectrum as well as various information theoretic measures are considered for Hulthén potential in D dimension. For a given ℓ≠0 state, analytic expressions are derived, following a simple intuitive approximation for accurate representation of centrifugal term, within the conventional Nikiforov-Uvarov method. This is derived from a linear combination of two widely used Greene-Aldrich and Pekeris-type approximations. Energy, wave function, normalization constant, expectation value in r and p space, Heisenberg uncertainty relation, entropic moment of order α¯, Shannon entropy, Rényi entropy, disequilibrium, majorization as well as four selected complexity measures like LMC (López-Ruiz, Mancini, Calbert), shape Rényi complexity, Generalized Rényi complexity and Rényi complexity ratio are offered for different screening parameters (δ). The effective potential is described quite satisfactorily throughout the whole domain. Obtained results are compared with theoretical energies available in literature, which shows excellent agreement. Performance of six different approximations to centrifugal term is critically discussed. An approximate analytical expression for critical screening for a specific state in arbitrary dimension is offered. Additionally, some inter-dimensional degeneracy occurring in two states, at different dimension for a particular δ is also uncovered. PACS: 02.60.-x, 03.65.Ca, 03.65.Ge, 03.65.-w Keywords: Hulthén potential, Rényi complexity ratio, Statistical complexity, Majorization, Pekeris approximation, Greene-Aldrich approximation.

Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential

In this study, an approximate solution of the Schr�dinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov�Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.

Study on the Applicability of Varshni Potential to Predict the Mass Spectra of the Quark-Antiquark Systems in a Non-relativistic Framework

In this work, we obtain the Schrödinger equation solutions for the Varshni potential using the Nikiforov-Uvarov method. The energy eigenvalues are obtained in non-relativistic regime. The corresponding eigenfunction is obtained in terms of Laguerre polynomials. We applied the present results to calculate heavy-meson masses of charmonium cc ¯ and bottomonium bb ¯. The mass spectra for charmonium and bottomonium multiplets have been predicted numerically. The results are in good agreement with experimental data and the works of other researchers. Keywords: Schrödinger equation, Varshni potential, Nikiforov-Uvarov method, Heavy meson. PACs: 14.20.Lq; 03.65.-w; 14.40.Pq; 11.80.Fv.

Vibrational energies of some diatomic molecules for a modified and deformed potential

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov-Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.